Math Lesson 10.1.3 - Double Inequalities and the Symbols used to Express Solution Sets

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Welcome to our Math lesson on Double Inequalities and the Symbols used to Express Solution Sets, this is the third lesson of our suite of math lessons covering the topic of Solving Linear Inequalities, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Double Inequalities and the Symbols used to Express Solution Sets

Sometimes we may encounter some special inequalities that contain two inequality symbols, consisting of an algebraic expression in-between, and numbers aside from these inequality symbols. In such cases, we are dealing with double inequalities. For example, 1 < x < 7 is a double inequality, as it expresses the inequality "the values of the variable x must be between 1 and 7 without including these limit values", which can be written in two separate parts, such as "x > 1" and "x < 7", where the solution set must include only numbers that make both these individual inequalities true.

Example 2

Write the following individual inequalities as a double inequality

1. x ≥ -2 and x < 9
2. x > 0 and x < 5

Solution 2

We must focus on the variable and read the double inequalities from there. The variable, however, must be in the middle of the sentence that contains the double inequality. In this way, we must invert laterally the direction of the first inequality. Hence, we obtain

1. x ≥ -2 and x < 9 → -2 ≤ x < 9
2. x > 0 and
   x < 5 → 0 < x < 5

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1. Double Inequalitie Feedback. Helps other - Leave a rating for this double inequalitie (see below)
2. Inequalities Math tutorial: Solving Linear Inequalities. Read the Solving Linear Inequalities math tutorial and build your math knowledge of Inequalities
3. Inequalities Video tutorial: Solving Linear Inequalities. Watch or listen to the Solving Linear Inequalities video tutorial, a useful way to help you revise when travelling to and from school/college
4. Inequalities Revision Notes: Solving Linear Inequalities. Print the notes so you can revise the key points covered in the math tutorial for Solving Linear Inequalities
5. Inequalities Practice Questions: Solving Linear Inequalities. Test and improve your knowledge of Solving Linear Inequalities with example questins and answers
6. Check your calculations for Inequalities questions with our excellent Inequalities calculators which contain full equations and calculations clearly displayed line by line. See the Inequalities Calculators by iCalculator™ below.
7. Continuing learning inequalities - read our next math tutorial: Quadratic Inequalities

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